# Variability of the Wind Turbine Power Curve

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## Abstract

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## 1. Introduction

## 2. Influence of Wind Speed Variability on Wind Power

## 3. Results and Discussion

## 4. Summary

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Instantaneous power $P(t)$ versus instantaneous wind speed $v(t)$ (solid grey circles) and time-averaged power $\overline{P}$ versus time-averaged wind speed $\overline{v}$ (solid red circles) for the Howard data set (Table 1). Considerable scatter in $P(t)$ versus $v(t)$ occurs about the time-averaged power curve. The scatter increases with mean speed $\overline{v}$, as qualitatively shown with blue arrows at $\overline{v}=$ 5, 7, and 9 m/s.

**Figure 2.**Statistical convergence of (

**a**) mean wind speed; and (

**b**) mean wind power versus number of samples contributing to the average. Each trace represents a separate data set generated with a bootstrap protocol by randomly shuffling values of the original Howard time series (Table 1). The averages approach asymptotic convergence around 400 samples.

**Figure 3.**(

**a**) log–log scale: The standard deviation of wind speed fluctuations ${\mathsf{\sigma}}_{v}$ (red solid circles) versus mean wind speed $\overline{v}$ and the standard deviation of wind power fluctuations ${\mathsf{\sigma}}_{P}$ (blue solid squares) versus mean wind power $\overline{P}$ for the Howard data set. Power-law fits to the data provided ${\mathsf{\sigma}}_{v}=0.25\times {\overline{v}}^{0.73}$ (solid line) and $3.9\times {\overline{P}}^{0.49}$ (dashed line); (

**b**) Whereas ${\mathsf{\sigma}}_{v}$ vs. $\overline{v}$ for Big Bear Lake (red solid circles) exhibits power-law scaling with a fit value of $0.4\times {\overline{v}}^{0.6}$ (solid line); and (

**c**) the Atacama data set (blue solid squares) reveals a monotonic increase in ${\mathsf{\sigma}}_{v}$ vs. $\overline{v}$. Although we include a power-law fit ${\mathsf{\sigma}}_{v}=0.31\times {\overline{v}}^{0.68}$ (dashed line) for illustrative purposes, the scatter in the data does not permit one to place any confidence in the fit value of the exponent.

Name | Location Coordinates | Elevation | Terrain | Duration | Sampling Rate |
---|---|---|---|---|---|

Howard, New York | 42.339693°, −77.569523° | 605 m | farm land | 20 Days | 0.2 Hz |

Big Bear Lake, California | 34.25836°, −116.92125° | 2085 m | forested | 12 Days | 1 Hz |

Atacama, Chile | −23.01667°, −67.75° | 5080 m | desert | 13 Days | 1 Hz |

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**MDPI and ACS Style**

Bandi, M.M.; Apt, J.
Variability of the Wind Turbine Power Curve. *Appl. Sci.* **2016**, *6*, 262.
https://doi.org/10.3390/app6090262

**AMA Style**

Bandi MM, Apt J.
Variability of the Wind Turbine Power Curve. *Applied Sciences*. 2016; 6(9):262.
https://doi.org/10.3390/app6090262

**Chicago/Turabian Style**

Bandi, Mahesh M., and Jay Apt.
2016. "Variability of the Wind Turbine Power Curve" *Applied Sciences* 6, no. 9: 262.
https://doi.org/10.3390/app6090262